A373276 - OEIS

%I #11 May 29 2024 13:46:37

%S 1,2,10,23,82,236,730,2156,6571,19604,59050,176918,531442,1593596,

%T 4783060,14346689,43046722,129133838,387420490,1162241726,3486785140,

%U 10460294156,31381059610,94143003584,282429536563,847288078004,2541865834900,7625595889958

%N a(n) = Sum_{d|n} (-1)^(d-1) * 3^(n/d-1).

%F G.f.: 1/3 * Sum_{k>=1} (3*x)^k / (1 + x^k).

%F If p is an odd prime, a(p) = 1 + 3^(p-1).

%o (PARI) a(n) = sumdiv(n, d, (-1)^(d-1)*3^(n/d-1));

%o (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, (3*x)^k/(1+x^k))/3)

%Y Cf. A048272, A373275.

%Y Cf. A321386, A357051.

%K nonn,easy

%O 1,2

%A _Seiichi Manyama_, May 29 2024